Properties

Label 560.2.ci.c.17.1
Level $560$
Weight $2$
Character 560.17
Analytic conductor $4.472$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 560.ci (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.47162251319\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 10 x^{14} + 61 x^{12} + 266 x^{10} + 852 x^{8} + 1438 x^{6} + 1933 x^{4} + 3038 x^{2} + 2401\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 17.1
Root \(0.144868 - 1.25092i\) of defining polynomial
Character \(\chi\) \(=\) 560.17
Dual form 560.2.ci.c.33.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.95290 + 0.523277i) q^{3} +(-1.82591 + 1.29076i) q^{5} +(1.90155 - 1.83959i) q^{7} +(0.941911 - 0.543813i) q^{9} +O(q^{10})\) \(q+(-1.95290 + 0.523277i) q^{3} +(-1.82591 + 1.29076i) q^{5} +(1.90155 - 1.83959i) q^{7} +(0.941911 - 0.543813i) q^{9} +(-2.01999 + 3.49872i) q^{11} +(-0.204875 - 0.204875i) q^{13} +(2.89039 - 3.47617i) q^{15} +(-0.527924 - 1.97024i) q^{17} +(-3.10166 - 5.37224i) q^{19} +(-2.75092 + 4.58757i) q^{21} +(4.38350 + 1.17456i) q^{23} +(1.66789 - 4.71361i) q^{25} +(2.73397 - 2.73397i) q^{27} -7.15869i q^{29} +(-6.33287 - 3.65628i) q^{31} +(2.11403 - 7.88965i) q^{33} +(-1.09759 + 5.81337i) q^{35} +(1.19723 - 4.46814i) q^{37} +(0.507306 + 0.292893i) q^{39} -2.58745i q^{41} +(4.97801 - 4.97801i) q^{43} +(-1.01791 + 2.20873i) q^{45} +(0.304388 + 0.0815604i) q^{47} +(0.231803 - 6.99616i) q^{49} +(2.06196 + 3.57142i) q^{51} +(2.14370 + 8.00039i) q^{53} +(-0.827689 - 8.99566i) q^{55} +(8.86840 + 8.86840i) q^{57} +(0.427702 - 0.740802i) q^{59} +(-5.99356 + 3.46038i) q^{61} +(0.790700 - 2.76682i) q^{63} +(0.638527 + 0.109639i) q^{65} +(-3.05106 + 0.817530i) q^{67} -9.17514 q^{69} -7.12240 q^{71} +(-11.1331 + 2.98311i) q^{73} +(-0.790684 + 10.0780i) q^{75} +(2.59511 + 10.3690i) q^{77} +(-4.39618 + 2.53813i) q^{79} +(-5.53997 + 9.59552i) q^{81} +(-3.85372 - 3.85372i) q^{83} +(3.50704 + 2.91605i) q^{85} +(3.74598 + 13.9802i) q^{87} +(1.53615 + 2.66069i) q^{89} +(-0.766467 - 0.0126942i) q^{91} +(14.2807 + 3.82650i) q^{93} +(12.5976 + 5.80572i) q^{95} +(6.63103 - 6.63103i) q^{97} +4.39398i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 12q^{5} - 8q^{7} + O(q^{10}) \) \( 16q - 12q^{5} - 8q^{7} + 12q^{11} - 16q^{15} - 36q^{17} - 28q^{21} + 4q^{23} + 12q^{25} - 24q^{31} + 48q^{33} - 8q^{35} + 4q^{37} + 8q^{43} - 12q^{45} - 12q^{47} + 16q^{51} - 28q^{53} + 8q^{57} - 12q^{61} + 36q^{63} - 8q^{65} - 32q^{67} - 16q^{71} - 12q^{73} + 48q^{75} + 16q^{77} + 24q^{85} + 24q^{87} + 16q^{91} + 28q^{93} - 20q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(351\) \(421\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.95290 + 0.523277i −1.12751 + 0.302114i −0.773917 0.633287i \(-0.781705\pi\)
−0.353588 + 0.935401i \(0.615039\pi\)
\(4\) 0 0
\(5\) −1.82591 + 1.29076i −0.816571 + 0.577245i
\(6\) 0 0
\(7\) 1.90155 1.83959i 0.718719 0.695300i
\(8\) 0 0
\(9\) 0.941911 0.543813i 0.313970 0.181271i
\(10\) 0 0
\(11\) −2.01999 + 3.49872i −0.609049 + 1.05490i 0.382349 + 0.924018i \(0.375115\pi\)
−0.991397 + 0.130886i \(0.958218\pi\)
\(12\) 0 0
\(13\) −0.204875 0.204875i −0.0568221 0.0568221i 0.678125 0.734947i \(-0.262793\pi\)
−0.734947 + 0.678125i \(0.762793\pi\)
\(14\) 0 0
\(15\) 2.89039 3.47617i 0.746295 0.897544i
\(16\) 0 0
\(17\) −0.527924 1.97024i −0.128040 0.477853i 0.871890 0.489703i \(-0.162895\pi\)
−0.999930 + 0.0118498i \(0.996228\pi\)
\(18\) 0 0
\(19\) −3.10166 5.37224i −0.711571 1.23248i −0.964267 0.264931i \(-0.914651\pi\)
0.252697 0.967545i \(-0.418682\pi\)
\(20\) 0 0
\(21\) −2.75092 + 4.58757i −0.600300 + 1.00109i
\(22\) 0 0
\(23\) 4.38350 + 1.17456i 0.914023 + 0.244912i 0.685029 0.728516i \(-0.259790\pi\)
0.228994 + 0.973428i \(0.426456\pi\)
\(24\) 0 0
\(25\) 1.66789 4.71361i 0.333577 0.942723i
\(26\) 0 0
\(27\) 2.73397 2.73397i 0.526152 0.526152i
\(28\) 0 0
\(29\) 7.15869i 1.32934i −0.747139 0.664668i \(-0.768573\pi\)
0.747139 0.664668i \(-0.231427\pi\)
\(30\) 0 0
\(31\) −6.33287 3.65628i −1.13742 0.656688i −0.191627 0.981468i \(-0.561376\pi\)
−0.945790 + 0.324780i \(0.894710\pi\)
\(32\) 0 0
\(33\) 2.11403 7.88965i 0.368005 1.37341i
\(34\) 0 0
\(35\) −1.09759 + 5.81337i −0.185527 + 0.982639i
\(36\) 0 0
\(37\) 1.19723 4.46814i 0.196824 0.734558i −0.794963 0.606658i \(-0.792510\pi\)
0.991787 0.127900i \(-0.0408236\pi\)
\(38\) 0 0
\(39\) 0.507306 + 0.292893i 0.0812340 + 0.0469005i
\(40\) 0 0
\(41\) 2.58745i 0.404093i −0.979376 0.202046i \(-0.935241\pi\)
0.979376 0.202046i \(-0.0647591\pi\)
\(42\) 0 0
\(43\) 4.97801 4.97801i 0.759140 0.759140i −0.217026 0.976166i \(-0.569636\pi\)
0.976166 + 0.217026i \(0.0696356\pi\)
\(44\) 0 0
\(45\) −1.01791 + 2.20873i −0.151742 + 0.329258i
\(46\) 0 0
\(47\) 0.304388 + 0.0815604i 0.0443995 + 0.0118968i 0.280950 0.959722i \(-0.409350\pi\)
−0.236551 + 0.971619i \(0.576017\pi\)
\(48\) 0 0
\(49\) 0.231803 6.99616i 0.0331148 0.999452i
\(50\) 0 0
\(51\) 2.06196 + 3.57142i 0.288732 + 0.500099i
\(52\) 0 0
\(53\) 2.14370 + 8.00039i 0.294460 + 1.09894i 0.941646 + 0.336606i \(0.109279\pi\)
−0.647186 + 0.762332i \(0.724054\pi\)
\(54\) 0 0
\(55\) −0.827689 8.99566i −0.111606 1.21297i
\(56\) 0 0
\(57\) 8.86840 + 8.86840i 1.17465 + 1.17465i
\(58\) 0 0
\(59\) 0.427702 0.740802i 0.0556821 0.0964442i −0.836841 0.547446i \(-0.815600\pi\)
0.892523 + 0.451002i \(0.148933\pi\)
\(60\) 0 0
\(61\) −5.99356 + 3.46038i −0.767397 + 0.443057i −0.831945 0.554858i \(-0.812773\pi\)
0.0645484 + 0.997915i \(0.479439\pi\)
\(62\) 0 0
\(63\) 0.790700 2.76682i 0.0996189 0.348587i
\(64\) 0 0
\(65\) 0.638527 + 0.109639i 0.0791995 + 0.0135990i
\(66\) 0 0
\(67\) −3.05106 + 0.817530i −0.372747 + 0.0998772i −0.440329 0.897837i \(-0.645138\pi\)
0.0675822 + 0.997714i \(0.478472\pi\)
\(68\) 0 0
\(69\) −9.17514 −1.10456
\(70\) 0 0
\(71\) −7.12240 −0.845273 −0.422637 0.906299i \(-0.638895\pi\)
−0.422637 + 0.906299i \(0.638895\pi\)
\(72\) 0 0
\(73\) −11.1331 + 2.98311i −1.30303 + 0.349147i −0.842597 0.538545i \(-0.818974\pi\)
−0.460438 + 0.887692i \(0.652307\pi\)
\(74\) 0 0
\(75\) −0.790684 + 10.0780i −0.0913004 + 1.16370i
\(76\) 0 0
\(77\) 2.59511 + 10.3690i 0.295740 + 1.18165i
\(78\) 0 0
\(79\) −4.39618 + 2.53813i −0.494609 + 0.285562i −0.726484 0.687183i \(-0.758847\pi\)
0.231876 + 0.972745i \(0.425514\pi\)
\(80\) 0 0
\(81\) −5.53997 + 9.59552i −0.615553 + 1.06617i
\(82\) 0 0
\(83\) −3.85372 3.85372i −0.423001 0.423001i 0.463235 0.886236i \(-0.346689\pi\)
−0.886236 + 0.463235i \(0.846689\pi\)
\(84\) 0 0
\(85\) 3.50704 + 2.91605i 0.380392 + 0.316290i
\(86\) 0 0
\(87\) 3.74598 + 13.9802i 0.401611 + 1.49883i
\(88\) 0 0
\(89\) 1.53615 + 2.66069i 0.162832 + 0.282033i 0.935883 0.352310i \(-0.114604\pi\)
−0.773051 + 0.634343i \(0.781271\pi\)
\(90\) 0 0
\(91\) −0.766467 0.0126942i −0.0803475 0.00133071i
\(92\) 0 0
\(93\) 14.2807 + 3.82650i 1.48084 + 0.396789i
\(94\) 0 0
\(95\) 12.5976 + 5.80572i 1.29249 + 0.595655i
\(96\) 0 0
\(97\) 6.63103 6.63103i 0.673279 0.673279i −0.285191 0.958471i \(-0.592057\pi\)
0.958471 + 0.285191i \(0.0920572\pi\)
\(98\) 0 0
\(99\) 4.39398i 0.441611i
\(100\) 0 0
\(101\) −8.56364 4.94422i −0.852114 0.491968i 0.00924966 0.999957i \(-0.497056\pi\)
−0.861364 + 0.507989i \(0.830389\pi\)
\(102\) 0 0
\(103\) −1.10827 + 4.13612i −0.109201 + 0.407544i −0.998788 0.0492221i \(-0.984326\pi\)
0.889587 + 0.456766i \(0.150992\pi\)
\(104\) 0 0
\(105\) −0.898518 11.9273i −0.0876864 1.16398i
\(106\) 0 0
\(107\) 3.84918 14.3653i 0.372114 1.38875i −0.485402 0.874291i \(-0.661327\pi\)
0.857516 0.514457i \(-0.172007\pi\)
\(108\) 0 0
\(109\) 11.4586 + 6.61564i 1.09754 + 0.633664i 0.935573 0.353133i \(-0.114884\pi\)
0.161964 + 0.986797i \(0.448217\pi\)
\(110\) 0 0
\(111\) 9.35230i 0.887681i
\(112\) 0 0
\(113\) 9.75336 9.75336i 0.917519 0.917519i −0.0793296 0.996848i \(-0.525278\pi\)
0.996848 + 0.0793296i \(0.0252780\pi\)
\(114\) 0 0
\(115\) −9.51994 + 3.51341i −0.887739 + 0.327627i
\(116\) 0 0
\(117\) −0.304388 0.0815604i −0.0281406 0.00754026i
\(118\) 0 0
\(119\) −4.62831 2.77535i −0.424276 0.254416i
\(120\) 0 0
\(121\) −2.66069 4.60846i −0.241881 0.418951i
\(122\) 0 0
\(123\) 1.35396 + 5.05303i 0.122082 + 0.455617i
\(124\) 0 0
\(125\) 3.03873 + 10.7595i 0.271792 + 0.962356i
\(126\) 0 0
\(127\) 2.19984 + 2.19984i 0.195204 + 0.195204i 0.797940 0.602736i \(-0.205923\pi\)
−0.602736 + 0.797940i \(0.705923\pi\)
\(128\) 0 0
\(129\) −7.11667 + 12.3264i −0.626587 + 1.08528i
\(130\) 0 0
\(131\) 6.32091 3.64938i 0.552260 0.318848i −0.197773 0.980248i \(-0.563371\pi\)
0.750033 + 0.661400i \(0.230037\pi\)
\(132\) 0 0
\(133\) −15.7807 4.50980i −1.36836 0.391049i
\(134\) 0 0
\(135\) −1.46309 + 8.52087i −0.125922 + 0.733360i
\(136\) 0 0
\(137\) −6.93431 + 1.85804i −0.592438 + 0.158743i −0.542567 0.840012i \(-0.682548\pi\)
−0.0498710 + 0.998756i \(0.515881\pi\)
\(138\) 0 0
\(139\) 12.4172 1.05321 0.526605 0.850110i \(-0.323465\pi\)
0.526605 + 0.850110i \(0.323465\pi\)
\(140\) 0 0
\(141\) −0.637116 −0.0536549
\(142\) 0 0
\(143\) 1.13064 0.302955i 0.0945492 0.0253344i
\(144\) 0 0
\(145\) 9.24014 + 13.0711i 0.767352 + 1.08550i
\(146\) 0 0
\(147\) 3.20824 + 13.7841i 0.264611 + 1.13689i
\(148\) 0 0
\(149\) −20.7399 + 11.9742i −1.69908 + 0.980963i −0.752440 + 0.658661i \(0.771123\pi\)
−0.946637 + 0.322302i \(0.895543\pi\)
\(150\) 0 0
\(151\) −1.77167 + 3.06862i −0.144176 + 0.249721i −0.929065 0.369916i \(-0.879387\pi\)
0.784889 + 0.619636i \(0.212720\pi\)
\(152\) 0 0
\(153\) −1.56870 1.56870i −0.126822 0.126822i
\(154\) 0 0
\(155\) 16.2826 1.49816i 1.30785 0.120335i
\(156\) 0 0
\(157\) −1.58462 5.91389i −0.126467 0.471980i 0.873421 0.486966i \(-0.161896\pi\)
−0.999888 + 0.0149859i \(0.995230\pi\)
\(158\) 0 0
\(159\) −8.37284 14.5022i −0.664010 1.15010i
\(160\) 0 0
\(161\) 10.4962 5.83037i 0.827213 0.459498i
\(162\) 0 0
\(163\) −15.9937 4.28549i −1.25272 0.335666i −0.429334 0.903146i \(-0.641252\pi\)
−0.823387 + 0.567480i \(0.807918\pi\)
\(164\) 0 0
\(165\) 6.32361 + 17.1345i 0.492293 + 1.33392i
\(166\) 0 0
\(167\) −10.2873 + 10.2873i −0.796056 + 0.796056i −0.982471 0.186415i \(-0.940313\pi\)
0.186415 + 0.982471i \(0.440313\pi\)
\(168\) 0 0
\(169\) 12.9161i 0.993543i
\(170\) 0 0
\(171\) −5.84298 3.37345i −0.446824 0.257974i
\(172\) 0 0
\(173\) 2.01155 7.50720i 0.152935 0.570762i −0.846338 0.532646i \(-0.821198\pi\)
0.999273 0.0381159i \(-0.0121356\pi\)
\(174\) 0 0
\(175\) −5.49955 12.0314i −0.415727 0.909489i
\(176\) 0 0
\(177\) −0.447613 + 1.67052i −0.0336447 + 0.125564i
\(178\) 0 0
\(179\) 3.34695 + 1.93236i 0.250163 + 0.144431i 0.619839 0.784729i \(-0.287198\pi\)
−0.369676 + 0.929161i \(0.620531\pi\)
\(180\) 0 0
\(181\) 6.99107i 0.519642i 0.965657 + 0.259821i \(0.0836636\pi\)
−0.965657 + 0.259821i \(0.916336\pi\)
\(182\) 0 0
\(183\) 9.89407 9.89407i 0.731390 0.731390i
\(184\) 0 0
\(185\) 3.58125 + 9.70376i 0.263299 + 0.713435i
\(186\) 0 0
\(187\) 7.95971 + 2.13280i 0.582071 + 0.155966i
\(188\) 0 0
\(189\) 0.169398 10.2282i 0.0123219 0.743990i
\(190\) 0 0
\(191\) 2.23721 + 3.87496i 0.161879 + 0.280383i 0.935543 0.353214i \(-0.114911\pi\)
−0.773664 + 0.633597i \(0.781578\pi\)
\(192\) 0 0
\(193\) −5.19573 19.3907i −0.373997 1.39577i −0.854805 0.518949i \(-0.826324\pi\)
0.480809 0.876825i \(-0.340343\pi\)
\(194\) 0 0
\(195\) −1.30435 + 0.120013i −0.0934064 + 0.00859431i
\(196\) 0 0
\(197\) −7.84901 7.84901i −0.559219 0.559219i 0.369866 0.929085i \(-0.379404\pi\)
−0.929085 + 0.369866i \(0.879404\pi\)
\(198\) 0 0
\(199\) −5.40103 + 9.35485i −0.382869 + 0.663148i −0.991471 0.130327i \(-0.958397\pi\)
0.608602 + 0.793475i \(0.291730\pi\)
\(200\) 0 0
\(201\) 5.53062 3.19310i 0.390100 0.225224i
\(202\) 0 0
\(203\) −13.1691 13.6126i −0.924288 0.955419i
\(204\) 0 0
\(205\) 3.33978 + 4.72446i 0.233260 + 0.329970i
\(206\) 0 0
\(207\) 4.76761 1.27748i 0.331372 0.0887908i
\(208\) 0 0
\(209\) 25.0613 1.73353
\(210\) 0 0
\(211\) −7.56555 −0.520834 −0.260417 0.965496i \(-0.583860\pi\)
−0.260417 + 0.965496i \(0.583860\pi\)
\(212\) 0 0
\(213\) 13.9093 3.72699i 0.953050 0.255369i
\(214\) 0 0
\(215\) −2.66399 + 15.5148i −0.181682 + 1.05810i
\(216\) 0 0
\(217\) −18.7683 + 4.69728i −1.27408 + 0.318872i
\(218\) 0 0
\(219\) 20.1809 11.6514i 1.36370 0.787330i
\(220\) 0 0
\(221\) −0.295494 + 0.511811i −0.0198771 + 0.0344281i
\(222\) 0 0
\(223\) 9.35230 + 9.35230i 0.626277 + 0.626277i 0.947129 0.320853i \(-0.103969\pi\)
−0.320853 + 0.947129i \(0.603969\pi\)
\(224\) 0 0
\(225\) −0.992322 5.34682i −0.0661548 0.356455i
\(226\) 0 0
\(227\) −4.19127 15.6420i −0.278184 1.03820i −0.953677 0.300832i \(-0.902736\pi\)
0.675493 0.737367i \(-0.263931\pi\)
\(228\) 0 0
\(229\) −5.88820 10.1987i −0.389103 0.673947i 0.603226 0.797570i \(-0.293882\pi\)
−0.992329 + 0.123624i \(0.960548\pi\)
\(230\) 0 0
\(231\) −10.4938 18.8915i −0.690442 1.24297i
\(232\) 0 0
\(233\) 5.52920 + 1.48154i 0.362230 + 0.0970591i 0.435343 0.900264i \(-0.356627\pi\)
−0.0731138 + 0.997324i \(0.523294\pi\)
\(234\) 0 0
\(235\) −0.661059 + 0.243969i −0.0431227 + 0.0159148i
\(236\) 0 0
\(237\) 7.25713 7.25713i 0.471402 0.471402i
\(238\) 0 0
\(239\) 8.33794i 0.539337i −0.962953 0.269668i \(-0.913086\pi\)
0.962953 0.269668i \(-0.0869141\pi\)
\(240\) 0 0
\(241\) 2.56723 + 1.48219i 0.165370 + 0.0954763i 0.580401 0.814331i \(-0.302896\pi\)
−0.415031 + 0.909807i \(0.636229\pi\)
\(242\) 0 0
\(243\) 2.79578 10.4340i 0.179349 0.669340i
\(244\) 0 0
\(245\) 8.60710 + 13.0736i 0.549887 + 0.835239i
\(246\) 0 0
\(247\) −0.465184 + 1.73609i −0.0295989 + 0.110465i
\(248\) 0 0
\(249\) 9.54248 + 5.50936i 0.604730 + 0.349141i
\(250\) 0 0
\(251\) 16.1800i 1.02127i 0.859796 + 0.510637i \(0.170590\pi\)
−0.859796 + 0.510637i \(0.829410\pi\)
\(252\) 0 0
\(253\) −12.9641 + 12.9641i −0.815043 + 0.815043i
\(254\) 0 0
\(255\) −8.37479 3.85960i −0.524450 0.241697i
\(256\) 0 0
\(257\) −5.62621 1.50754i −0.350954 0.0940377i 0.0790355 0.996872i \(-0.474816\pi\)
−0.429989 + 0.902834i \(0.641483\pi\)
\(258\) 0 0
\(259\) −5.94295 10.6988i −0.369277 0.664793i
\(260\) 0 0
\(261\) −3.89299 6.74285i −0.240970 0.417372i
\(262\) 0 0
\(263\) −0.449601 1.67793i −0.0277236 0.103466i 0.950678 0.310180i \(-0.100389\pi\)
−0.978401 + 0.206715i \(0.933723\pi\)
\(264\) 0 0
\(265\) −14.2408 11.8410i −0.874803 0.727386i
\(266\) 0 0
\(267\) −4.39223 4.39223i −0.268800 0.268800i
\(268\) 0 0
\(269\) 1.89169 3.27650i 0.115338 0.199772i −0.802577 0.596549i \(-0.796538\pi\)
0.917915 + 0.396777i \(0.129872\pi\)
\(270\) 0 0
\(271\) 18.4029 10.6249i 1.11789 0.645416i 0.177032 0.984205i \(-0.443351\pi\)
0.940862 + 0.338789i \(0.110017\pi\)
\(272\) 0 0
\(273\) 1.50347 0.376284i 0.0909943 0.0227737i
\(274\) 0 0
\(275\) 13.1225 + 15.3569i 0.791317 + 0.926056i
\(276\) 0 0
\(277\) 4.72353 1.26567i 0.283810 0.0760465i −0.114106 0.993469i \(-0.536400\pi\)
0.397916 + 0.917422i \(0.369734\pi\)
\(278\) 0 0
\(279\) −7.95333 −0.476153
\(280\) 0 0
\(281\) −29.4776 −1.75849 −0.879243 0.476373i \(-0.841951\pi\)
−0.879243 + 0.476373i \(0.841951\pi\)
\(282\) 0 0
\(283\) 10.8991 2.92041i 0.647886 0.173601i 0.0801133 0.996786i \(-0.474472\pi\)
0.567773 + 0.823185i \(0.307805\pi\)
\(284\) 0 0
\(285\) −27.6399 4.74593i −1.63724 0.281125i
\(286\) 0 0
\(287\) −4.75986 4.92018i −0.280966 0.290429i
\(288\) 0 0
\(289\) 11.1193 6.41973i 0.654076 0.377631i
\(290\) 0 0
\(291\) −9.47985 + 16.4196i −0.555719 + 0.962533i
\(292\) 0 0
\(293\) 7.23407 + 7.23407i 0.422619 + 0.422619i 0.886105 0.463485i \(-0.153401\pi\)
−0.463485 + 0.886105i \(0.653401\pi\)
\(294\) 0 0
\(295\) 0.175251 + 1.90470i 0.0102035 + 0.110896i
\(296\) 0 0
\(297\) 4.04281 + 15.0880i 0.234588 + 0.875493i
\(298\) 0 0
\(299\) −0.657432 1.13871i −0.0380203 0.0658531i
\(300\) 0 0
\(301\) 0.308440 18.6235i 0.0177782 1.07344i
\(302\) 0 0
\(303\) 19.3111 + 5.17439i 1.10939 + 0.297261i
\(304\) 0 0
\(305\) 6.47718 14.0546i 0.370882 0.804763i
\(306\) 0 0
\(307\) −1.07859 + 1.07859i −0.0615584 + 0.0615584i −0.737216 0.675657i \(-0.763860\pi\)
0.675657 + 0.737216i \(0.263860\pi\)
\(308\) 0 0
\(309\) 8.65735i 0.492500i
\(310\) 0 0
\(311\) 8.33830 + 4.81412i 0.472821 + 0.272984i 0.717420 0.696641i \(-0.245323\pi\)
−0.244599 + 0.969624i \(0.578656\pi\)
\(312\) 0 0
\(313\) 0.783378 2.92361i 0.0442791 0.165252i −0.940246 0.340496i \(-0.889405\pi\)
0.984525 + 0.175244i \(0.0560716\pi\)
\(314\) 0 0
\(315\) 2.12755 + 6.07257i 0.119874 + 0.342150i
\(316\) 0 0
\(317\) 0.504353 1.88227i 0.0283273 0.105719i −0.950315 0.311291i \(-0.899239\pi\)
0.978642 + 0.205572i \(0.0659054\pi\)
\(318\) 0 0
\(319\) 25.0463 + 14.4605i 1.40232 + 0.809631i
\(320\) 0 0
\(321\) 30.0682i 1.67824i
\(322\) 0 0
\(323\) −8.94715 + 8.94715i −0.497833 + 0.497833i
\(324\) 0 0
\(325\) −1.30741 + 0.623993i −0.0725220 + 0.0346129i
\(326\) 0 0
\(327\) −25.8393 6.92363i −1.42892 0.382878i
\(328\) 0 0
\(329\) 0.728847 0.404858i 0.0401826 0.0223205i
\(330\) 0 0
\(331\) −14.4468 25.0225i −0.794066 1.37536i −0.923431 0.383765i \(-0.874627\pi\)
0.129365 0.991597i \(-0.458706\pi\)
\(332\) 0 0
\(333\) −1.30214 4.85966i −0.0713570 0.266308i
\(334\) 0 0
\(335\) 4.51573 5.43092i 0.246721 0.296723i
\(336\) 0 0
\(337\) −0.823226 0.823226i −0.0448440 0.0448440i 0.684329 0.729173i \(-0.260095\pi\)
−0.729173 + 0.684329i \(0.760095\pi\)
\(338\) 0 0
\(339\) −13.9436 + 24.1510i −0.757312 + 1.31170i
\(340\) 0 0
\(341\) 25.5846 14.7713i 1.38548 0.799910i
\(342\) 0 0
\(343\) −12.4293 13.7300i −0.671119 0.741350i
\(344\) 0 0
\(345\) 16.7530 11.8429i 0.901950 0.637600i
\(346\) 0 0
\(347\) −16.1350 + 4.32336i −0.866172 + 0.232090i −0.664432 0.747349i \(-0.731326\pi\)
−0.201740 + 0.979439i \(0.564660\pi\)
\(348\) 0 0
\(349\) −36.7146 −1.96529 −0.982644 0.185503i \(-0.940608\pi\)
−0.982644 + 0.185503i \(0.940608\pi\)
\(350\) 0 0
\(351\) −1.12024 −0.0597942
\(352\) 0 0
\(353\) −13.7845 + 3.69356i −0.733677 + 0.196588i −0.606266 0.795262i \(-0.707333\pi\)
−0.127411 + 0.991850i \(0.540667\pi\)
\(354\) 0 0
\(355\) 13.0048 9.19329i 0.690226 0.487929i
\(356\) 0 0
\(357\) 10.4909 + 2.99808i 0.555236 + 0.158675i
\(358\) 0 0
\(359\) −23.4596 + 13.5444i −1.23815 + 0.714847i −0.968716 0.248172i \(-0.920170\pi\)
−0.269435 + 0.963019i \(0.586837\pi\)
\(360\) 0 0
\(361\) −9.74064 + 16.8713i −0.512665 + 0.887962i
\(362\) 0 0
\(363\) 7.60756 + 7.60756i 0.399293 + 0.399293i
\(364\) 0 0
\(365\) 16.4776 19.8171i 0.862477 1.03727i
\(366\) 0 0
\(367\) −5.86782 21.8990i −0.306298 1.14312i −0.931823 0.362914i \(-0.881782\pi\)
0.625525 0.780204i \(-0.284885\pi\)
\(368\) 0 0
\(369\) −1.40709 2.43715i −0.0732502 0.126873i
\(370\) 0 0
\(371\) 18.7938 + 11.2696i 0.975726 + 0.585090i
\(372\) 0 0
\(373\) 12.3984 + 3.32215i 0.641966 + 0.172014i 0.565094 0.825027i \(-0.308840\pi\)
0.0768720 + 0.997041i \(0.475507\pi\)
\(374\) 0 0
\(375\) −11.5645 19.4220i −0.597188 1.00295i
\(376\) 0 0
\(377\) −1.46664 + 1.46664i −0.0755356 + 0.0755356i
\(378\) 0 0
\(379\) 14.4739i 0.743476i −0.928338 0.371738i \(-0.878762\pi\)
0.928338 0.371738i \(-0.121238\pi\)
\(380\) 0 0
\(381\) −5.44718 3.14493i −0.279068 0.161120i
\(382\) 0 0
\(383\) −0.453341 + 1.69189i −0.0231647 + 0.0864517i −0.976540 0.215334i \(-0.930916\pi\)
0.953376 + 0.301786i \(0.0975827\pi\)
\(384\) 0 0
\(385\) −18.1222 15.5831i −0.923595 0.794189i
\(386\) 0 0
\(387\) 1.98174 7.39595i 0.100737 0.375957i
\(388\) 0 0
\(389\) 2.40954 + 1.39115i 0.122169 + 0.0705341i 0.559839 0.828601i \(-0.310863\pi\)
−0.437670 + 0.899135i \(0.644196\pi\)
\(390\) 0 0
\(391\) 9.25661i 0.468127i
\(392\) 0 0
\(393\) −10.4344 + 10.4344i −0.526348 + 0.526348i
\(394\) 0 0
\(395\) 4.75090 10.3088i 0.239044 0.518692i
\(396\) 0 0
\(397\) 38.3163 + 10.2668i 1.92304 + 0.515277i 0.986212 + 0.165486i \(0.0529193\pi\)
0.936828 + 0.349791i \(0.113747\pi\)
\(398\) 0 0
\(399\) 33.1780 + 0.549491i 1.66098 + 0.0275089i
\(400\) 0 0
\(401\) 9.98528 + 17.2950i 0.498641 + 0.863672i 0.999999 0.00156835i \(-0.000499221\pi\)
−0.501358 + 0.865240i \(0.667166\pi\)
\(402\) 0 0
\(403\) 0.548365 + 2.04653i 0.0273160 + 0.101945i
\(404\) 0 0
\(405\) −2.27000 24.6713i −0.112797 1.22593i
\(406\) 0 0
\(407\) 13.2144 + 13.2144i 0.655012 + 0.655012i
\(408\) 0 0
\(409\) 7.65280 13.2550i 0.378407 0.655419i −0.612424 0.790529i \(-0.709805\pi\)
0.990831 + 0.135110i \(0.0431388\pi\)
\(410\) 0 0
\(411\) 12.5697 7.25713i 0.620019 0.357968i
\(412\) 0 0
\(413\) −0.549475 2.19547i −0.0270379 0.108032i
\(414\) 0 0
\(415\) 12.0108 + 2.06232i 0.589585 + 0.101235i
\(416\) 0 0
\(417\) −24.2495 + 6.49762i −1.18750 + 0.318190i
\(418\) 0 0
\(419\) −27.7027 −1.35337 −0.676684 0.736274i \(-0.736584\pi\)
−0.676684 + 0.736274i \(0.736584\pi\)
\(420\) 0 0
\(421\) 33.0159 1.60910 0.804549 0.593887i \(-0.202407\pi\)
0.804549 + 0.593887i \(0.202407\pi\)
\(422\) 0 0
\(423\) 0.331060 0.0887072i 0.0160967 0.00431309i
\(424\) 0 0
\(425\) −10.1675 0.797705i −0.493194 0.0386944i
\(426\) 0 0
\(427\) −5.03138 + 17.6058i −0.243485 + 0.852005i
\(428\) 0 0
\(429\) −2.04950 + 1.18328i −0.0989509 + 0.0571293i
\(430\) 0 0
\(431\) 11.9586 20.7129i 0.576027 0.997708i −0.419902 0.907569i \(-0.637936\pi\)
0.995929 0.0901384i \(-0.0287309\pi\)
\(432\) 0 0
\(433\) 13.2515 + 13.2515i 0.636829 + 0.636829i 0.949772 0.312943i \(-0.101315\pi\)
−0.312943 + 0.949772i \(0.601315\pi\)
\(434\) 0 0
\(435\) −24.8849 20.6914i −1.19314 0.992077i
\(436\) 0 0
\(437\) −7.28615 27.1923i −0.348544 1.30078i
\(438\) 0 0
\(439\) −7.05383 12.2176i −0.336661 0.583114i 0.647141 0.762370i \(-0.275964\pi\)
−0.983802 + 0.179256i \(0.942631\pi\)
\(440\) 0 0
\(441\) −3.58626 6.71582i −0.170774 0.319801i
\(442\) 0 0
\(443\) 20.3457 + 5.45161i 0.966652 + 0.259014i 0.707414 0.706800i \(-0.249862\pi\)
0.259238 + 0.965813i \(0.416528\pi\)
\(444\) 0 0
\(445\) −6.23919 2.87538i −0.295766 0.136306i
\(446\) 0 0
\(447\) 34.2370 34.2370i 1.61936 1.61936i
\(448\) 0 0
\(449\) 31.3247i 1.47831i 0.673538 + 0.739153i \(0.264774\pi\)
−0.673538 + 0.739153i \(0.735226\pi\)
\(450\) 0 0
\(451\) 9.05278 + 5.22662i 0.426279 + 0.246112i
\(452\) 0 0
\(453\) 1.85415 6.91977i 0.0871154 0.325119i
\(454\) 0 0
\(455\) 1.41588 0.966145i 0.0663776 0.0452936i
\(456\) 0 0
\(457\) −0.740622 + 2.76404i −0.0346448 + 0.129296i −0.981082 0.193591i \(-0.937987\pi\)
0.946438 + 0.322887i \(0.104653\pi\)
\(458\) 0 0
\(459\) −6.82989 3.94324i −0.318792 0.184055i
\(460\) 0 0
\(461\) 3.02674i 0.140969i 0.997513 + 0.0704846i \(0.0224546\pi\)
−0.997513 + 0.0704846i \(0.977545\pi\)
\(462\) 0 0
\(463\) −19.2889 + 19.2889i −0.896431 + 0.896431i −0.995118 0.0986876i \(-0.968536\pi\)
0.0986876 + 0.995118i \(0.468536\pi\)
\(464\) 0 0
\(465\) −31.0143 + 11.4461i −1.43825 + 0.530799i
\(466\) 0 0
\(467\) 24.2727 + 6.50385i 1.12321 + 0.300962i 0.772180 0.635403i \(-0.219166\pi\)
0.351026 + 0.936366i \(0.385833\pi\)
\(468\) 0 0
\(469\) −4.29784 + 7.16729i −0.198456 + 0.330955i
\(470\) 0 0
\(471\) 6.18921 + 10.7200i 0.285184 + 0.493953i
\(472\) 0 0
\(473\) 7.36115 + 27.4722i 0.338466 + 1.26317i
\(474\) 0 0
\(475\) −30.4959 + 5.65976i −1.39925 + 0.259688i
\(476\) 0 0
\(477\) 6.36989 + 6.36989i 0.291657 + 0.291657i
\(478\) 0 0
\(479\) −4.14346 + 7.17668i −0.189319 + 0.327911i −0.945024 0.327002i \(-0.893961\pi\)
0.755704 + 0.654913i \(0.227295\pi\)
\(480\) 0 0
\(481\) −1.16069 + 0.670127i −0.0529231 + 0.0305551i
\(482\) 0 0
\(483\) −17.4470 + 16.8785i −0.793867 + 0.767999i
\(484\) 0 0
\(485\) −3.54860 + 20.6667i −0.161134 + 0.938427i
\(486\) 0 0
\(487\) 10.3144 2.76375i 0.467392 0.125237i −0.0174340 0.999848i \(-0.505550\pi\)
0.484826 + 0.874611i \(0.338883\pi\)
\(488\) 0 0
\(489\) 33.4765 1.51386
\(490\) 0 0
\(491\) −25.7259 −1.16100 −0.580498 0.814262i \(-0.697142\pi\)
−0.580498 + 0.814262i \(0.697142\pi\)
\(492\) 0 0
\(493\) −14.1043 + 3.77924i −0.635227 + 0.170209i
\(494\) 0 0
\(495\) −5.67156 8.02300i −0.254918 0.360607i
\(496\) 0 0
\(497\) −13.5436 + 13.1023i −0.607514 + 0.587719i
\(498\) 0 0
\(499\) −12.6429 + 7.29940i −0.565975 + 0.326766i −0.755540 0.655102i \(-0.772626\pi\)
0.189565 + 0.981868i \(0.439292\pi\)
\(500\) 0 0
\(501\) 14.7069 25.4732i 0.657058 1.13806i
\(502\) 0 0
\(503\) 13.9891 + 13.9891i 0.623744 + 0.623744i 0.946487 0.322743i \(-0.104605\pi\)
−0.322743 + 0.946487i \(0.604605\pi\)
\(504\) 0 0
\(505\) 22.0182 2.02589i 0.979798 0.0901510i
\(506\) 0 0
\(507\) 6.75868 + 25.2237i 0.300163 + 1.12022i
\(508\) 0 0
\(509\) −1.42883 2.47481i −0.0633319 0.109694i 0.832621 0.553843i \(-0.186839\pi\)
−0.895953 + 0.444149i \(0.853506\pi\)
\(510\) 0 0
\(511\) −15.6825 + 26.1530i −0.693754 + 1.15694i
\(512\) 0 0
\(513\) −23.1674 6.20768i −1.02287 0.274076i
\(514\) 0 0
\(515\) −3.31513 8.98269i −0.146082 0.395825i
\(516\) 0 0
\(517\) −0.900216 + 0.900216i −0.0395914 + 0.0395914i
\(518\) 0 0
\(519\) 15.7134i 0.689741i
\(520\) 0 0
\(521\) 24.7917 + 14.3135i 1.08614 + 0.627084i 0.932547 0.361049i \(-0.117581\pi\)
0.153595 + 0.988134i \(0.450915\pi\)
\(522\) 0 0
\(523\) −8.17429 + 30.5069i −0.357437 + 1.33397i 0.519954 + 0.854195i \(0.325949\pi\)
−0.877390 + 0.479777i \(0.840717\pi\)
\(524\) 0 0
\(525\) 17.0358 + 20.6183i 0.743504 + 0.899857i
\(526\) 0 0
\(527\) −3.86048 + 14.4075i −0.168165 + 0.627600i
\(528\) 0 0
\(529\) −2.08308 1.20267i −0.0905687 0.0522899i
\(530\) 0 0
\(531\) 0.930359i 0.0403742i
\(532\) 0 0
\(533\) −0.530105 + 0.530105i −0.0229614 + 0.0229614i
\(534\) 0 0
\(535\) 11.5139 + 31.1981i 0.497790 + 1.34881i
\(536\) 0 0
\(537\) −7.54741 2.02232i −0.325695 0.0872696i
\(538\) 0 0
\(539\) 24.0094 + 14.9432i 1.03416 + 0.643648i
\(540\) 0 0
\(541\) −18.4994 32.0420i −0.795353 1.37759i −0.922615 0.385722i \(-0.873952\pi\)
0.127262 0.991869i \(-0.459381\pi\)
\(542\) 0 0
\(543\) −3.65827 13.6528i −0.156991 0.585899i
\(544\) 0 0
\(545\) −29.4616 + 2.71076i −1.26200 + 0.116116i
\(546\) 0 0
\(547\) 20.0765 + 20.0765i 0.858409 + 0.858409i 0.991151 0.132742i \(-0.0423781\pi\)
−0.132742 + 0.991151i \(0.542378\pi\)
\(548\) 0 0
\(549\) −3.76360 + 6.51875i −0.160627 + 0.278213i
\(550\) 0 0
\(551\) −38.4582 + 22.2039i −1.63838 + 0.945916i
\(552\) 0 0
\(553\) −3.69043 + 12.9136i −0.156933 + 0.549141i
\(554\) 0 0
\(555\) −12.0716 17.0765i −0.512409 0.724855i
\(556\) 0 0
\(557\) 24.8367 6.65499i 1.05237 0.281981i 0.309137 0.951017i \(-0.399960\pi\)
0.743229 + 0.669037i \(0.233293\pi\)
\(558\) 0 0
\(559\) −2.03974 −0.0862718
\(560\) 0 0
\(561\) −16.6605 −0.703408
\(562\) 0 0
\(563\) −5.18407 + 1.38907i −0.218482 + 0.0585422i −0.366400 0.930458i \(-0.619410\pi\)
0.147917 + 0.989000i \(0.452743\pi\)
\(564\) 0 0
\(565\) −5.21952 + 30.3980i −0.219587 + 1.27885i
\(566\) 0 0
\(567\) 7.11728 + 28.4377i 0.298898 + 1.19427i
\(568\) 0 0
\(569\) −22.0839 + 12.7502i −0.925806 + 0.534514i −0.885483 0.464672i \(-0.846172\pi\)
−0.0403234 + 0.999187i \(0.512839\pi\)
\(570\) 0 0
\(571\) 7.95235 13.7739i 0.332795 0.576419i −0.650263 0.759709i \(-0.725341\pi\)
0.983059 + 0.183290i \(0.0586748\pi\)
\(572\) 0 0
\(573\) −6.39672 6.39672i −0.267227 0.267227i
\(574\) 0 0
\(575\) 12.8476 18.7031i 0.535781 0.779973i
\(576\) 0 0
\(577\) −5.96565 22.2641i −0.248353 0.926867i −0.971668 0.236349i \(-0.924049\pi\)
0.723315 0.690518i \(-0.242617\pi\)
\(578\) 0 0
\(579\) 20.2934 + 35.1493i 0.843366 + 1.46075i
\(580\) 0 0
\(581\) −14.4173 0.238779i −0.598132 0.00990621i
\(582\) 0 0
\(583\) −32.3214 8.66048i −1.33861 0.358681i
\(584\) 0 0
\(585\) 0.661059 0.243969i 0.0273314 0.0100869i
\(586\) 0 0
\(587\) 28.2277 28.2277i 1.16508 1.16508i 0.181734 0.983348i \(-0.441829\pi\)
0.983348 0.181734i \(-0.0581711\pi\)
\(588\) 0 0
\(589\) 45.3622i 1.86912i
\(590\) 0 0
\(591\) 19.4355 + 11.2211i 0.799471 + 0.461575i
\(592\) 0 0
\(593\) −9.16977 + 34.2220i −0.376557 + 1.40533i 0.474499 + 0.880256i \(0.342629\pi\)
−0.851056 + 0.525075i \(0.824037\pi\)
\(594\) 0 0
\(595\) 12.0332 0.906496i 0.493312 0.0371627i
\(596\) 0 0
\(597\) 5.65247 21.0953i 0.231340 0.863373i
\(598\) 0 0
\(599\) 14.5339 + 8.39115i 0.593839 + 0.342853i 0.766614 0.642108i \(-0.221940\pi\)
−0.172775 + 0.984961i \(0.555273\pi\)
\(600\) 0 0
\(601\) 1.73528i 0.0707833i 0.999374 + 0.0353917i \(0.0112679\pi\)
−0.999374 + 0.0353917i \(0.988732\pi\)
\(602\) 0 0
\(603\) −2.42925 + 2.42925i −0.0989266 + 0.0989266i
\(604\) 0 0
\(605\) 10.8066 + 4.98031i 0.439350 + 0.202478i
\(606\) 0 0
\(607\) −38.0930 10.2070i −1.54615 0.414288i −0.617900 0.786257i \(-0.712016\pi\)
−0.928245 + 0.371968i \(0.878683\pi\)
\(608\) 0 0
\(609\) 32.8410 + 19.6930i 1.33079 + 0.798000i
\(610\) 0 0
\(611\) −0.0456517 0.0790711i −0.00184687 0.00319887i
\(612\) 0 0
\(613\) 0.0885018 + 0.330293i 0.00357455 + 0.0133404i 0.967690 0.252143i \(-0.0811352\pi\)
−0.964116 + 0.265483i \(0.914469\pi\)
\(614\) 0 0
\(615\) −8.99444 7.47875i −0.362691 0.301572i
\(616\) 0 0
\(617\) 11.1876 + 11.1876i 0.450397 + 0.450397i 0.895486 0.445089i \(-0.146828\pi\)
−0.445089 + 0.895486i \(0.646828\pi\)
\(618\) 0 0
\(619\) 18.2682 31.6414i 0.734260 1.27178i −0.220787 0.975322i \(-0.570862\pi\)
0.955047 0.296454i \(-0.0958042\pi\)
\(620\) 0 0
\(621\) 15.1956 8.77316i 0.609777 0.352055i
\(622\) 0 0
\(623\) 7.81566 + 2.23356i 0.313128 + 0.0894855i
\(624\) 0 0
\(625\) −19.4363 15.7235i −0.777452 0.628942i
\(626\) 0 0
\(627\) −48.9421 + 13.1140i −1.95456 + 0.523723i
\(628\) 0 0
\(629\) −9.43535 −0.376212
\(630\) 0 0
\(631\) 35.8189 1.42593 0.712964 0.701201i \(-0.247352\pi\)
0.712964 + 0.701201i \(0.247352\pi\)
\(632\) 0 0
\(633\) 14.7747 3.95888i 0.587243 0.157351i
\(634\) 0 0
\(635\) −6.85616 1.17725i −0.272079 0.0467176i
\(636\) 0 0
\(637\) −1.48083 + 1.38585i −0.0586726 + 0.0549093i
\(638\) 0 0
\(639\) −6.70867 + 3.87325i −0.265391 + 0.153223i
\(640\) 0 0
\(641\) 7.16573 12.4114i 0.283029 0.490221i −0.689100 0.724666i \(-0.741994\pi\)
0.972129 + 0.234445i \(0.0753272\pi\)
\(642\) 0 0
\(643\) 7.65201 + 7.65201i 0.301766 + 0.301766i 0.841704 0.539939i \(-0.181553\pi\)
−0.539939 + 0.841704i \(0.681553\pi\)
\(644\) 0 0
\(645\) −2.91605 31.6928i −0.114819 1.24790i
\(646\) 0 0
\(647\) −8.37254 31.2468i −0.329159 1.22844i −0.910065 0.414466i \(-0.863968\pi\)
0.580906 0.813971i \(-0.302698\pi\)
\(648\) 0 0
\(649\) 1.72791 + 2.99282i 0.0678262 + 0.117478i
\(650\) 0 0
\(651\) 34.1947 18.9943i 1.34019 0.744447i
\(652\) 0 0
\(653\) 0.494788 + 0.132578i 0.0193625 + 0.00518818i 0.268487 0.963283i \(-0.413476\pi\)
−0.249125 + 0.968471i \(0.580143\pi\)
\(654\) 0 0
\(655\) −6.83094 + 14.8222i −0.266907 + 0.579151i
\(656\) 0 0
\(657\) −8.86417 + 8.86417i −0.345824 + 0.345824i
\(658\) 0 0
\(659\) 19.5542i 0.761723i −0.924632 0.380862i \(-0.875627\pi\)
0.924632 0.380862i \(-0.124373\pi\)
\(660\) 0 0
\(661\) 34.0324 + 19.6486i 1.32371 + 0.764242i 0.984318 0.176405i \(-0.0564468\pi\)
0.339388 + 0.940647i \(0.389780\pi\)
\(662\) 0 0
\(663\) 0.309250 1.15414i 0.0120103 0.0448230i
\(664\) 0 0
\(665\) 34.6352 12.1346i 1.34310 0.470559i
\(666\) 0 0
\(667\) 8.40828 31.3801i 0.325570 1.21504i
\(668\) 0 0
\(669\) −23.1579 13.3702i −0.895337 0.516923i
\(670\) 0 0
\(671\) 27.9597i 1.07937i
\(672\) 0 0
\(673\) 18.4813 18.4813i 0.712401 0.712401i −0.254636 0.967037i \(-0.581956\pi\)
0.967037 + 0.254636i \(0.0819556\pi\)
\(674\) 0 0
\(675\) −8.32692 17.4468i −0.320503 0.671528i
\(676\) 0 0
\(677\) −39.7951 10.6631i −1.52945 0.409815i −0.606611 0.794999i \(-0.707472\pi\)
−0.922840 + 0.385183i \(0.874138\pi\)
\(678\) 0 0
\(679\) 0.410862 24.8076i 0.0157674 0.952030i
\(680\) 0 0
\(681\) 16.3702 + 28.3541i 0.627309 + 1.08653i
\(682\) 0 0
\(683\) 2.36248 + 8.81689i 0.0903978 + 0.337369i 0.996282 0.0861573i \(-0.0274588\pi\)
−0.905884 + 0.423526i \(0.860792\pi\)
\(684\) 0 0
\(685\) 10.2631 12.3431i 0.392134 0.471607i
\(686\) 0 0
\(687\) 16.8358 + 16.8358i 0.642325 + 0.642325i
\(688\) 0 0
\(689\) 1.19989 2.07827i 0.0457121 0.0791758i
\(690\) 0 0
\(691\) 41.9971 24.2470i 1.59765 0.922401i 0.605706 0.795689i \(-0.292891\pi\)
0.991940 0.126712i \(-0.0404424\pi\)
\(692\) 0 0
\(693\) 8.08313 + 8.35538i 0.307053 + 0.317395i
\(694\) 0 0
\(695\) −22.6726 + 16.0276i −0.860022 + 0.607960i
\(696\) 0 0
\(697\) −5.09790 + 1.36598i −0.193097 + 0.0517401i
\(698\) 0 0
\(699\) −11.5732 −0.437739
\(700\) 0 0
\(701\) −30.8898 −1.16669 −0.583347 0.812223i \(-0.698257\pi\)
−0.583347 + 0.812223i \(0.698257\pi\)
\(702\) 0 0
\(703\) −27.7173 + 7.42684i −1.04538 + 0.280109i
\(704\) 0 0
\(705\) 1.16332 0.822363i 0.0438130 0.0309720i
\(706\) 0 0
\(707\) −25.3796 + 6.35191i −0.954496 + 0.238888i
\(708\) 0 0
\(709\) 12.7354 7.35277i 0.478287 0.276139i −0.241416 0.970422i \(-0.577612\pi\)
0.719702 + 0.694283i \(0.244278\pi\)
\(710\) 0 0
\(711\) −2.76054 + 4.78140i −0.103528 + 0.179316i
\(712\) 0 0
\(713\) −23.4656 23.4656i −0.878795 0.878795i
\(714\) 0 0
\(715\) −1.67341 + 2.01256i −0.0625821 + 0.0752654i
\(716\) 0 0
\(717\) 4.36306 + 16.2831i 0.162941 + 0.608105i
\(718\) 0 0
\(719\) 11.7360 + 20.3273i 0.437679 + 0.758082i 0.997510 0.0705247i \(-0.0224674\pi\)
−0.559831 + 0.828607i \(0.689134\pi\)
\(720\) 0 0
\(721\) 5.50134 + 9.90382i 0.204881 + 0.368837i
\(722\) 0 0
\(723\) −5.78913 1.55119i −0.215300 0.0576895i
\(724\) 0 0
\(725\) −33.7433 11.9399i −1.25320 0.443436i
\(726\) 0 0
\(727\) −14.1380 + 14.1380i −0.524349 + 0.524349i −0.918882 0.394533i \(-0.870907\pi\)
0.394533 + 0.918882i \(0.370907\pi\)
\(728\) 0 0
\(729\) 11.4004i 0.422236i
\(730\) 0 0
\(731\) −12.4359 7.17986i −0.459958 0.265557i
\(732\) 0 0
\(733\) −7.17859 + 26.7908i −0.265147 + 0.989543i 0.697013 + 0.717058i \(0.254512\pi\)
−0.962160 + 0.272484i \(0.912155\pi\)
\(734\) 0 0
\(735\) −23.6499 21.0274i −0.872339 0.775608i
\(736\) 0 0
\(737\) 3.30280 12.3262i 0.121660 0.454042i
\(738\) 0 0
\(739\) −11.7451 6.78102i −0.432050 0.249444i 0.268170 0.963372i \(-0.413581\pi\)
−0.700219 + 0.713928i \(0.746915\pi\)
\(740\) 0 0
\(741\) 3.63383i 0.133492i
\(742\) 0 0
\(743\) −13.5961 + 13.5961i −0.498791 + 0.498791i −0.911062 0.412270i \(-0.864736\pi\)
0.412270 + 0.911062i \(0.364736\pi\)
\(744\) 0 0
\(745\) 22.4134 48.6339i 0.821162 1.78181i
\(746\) 0 0
\(747\) −5.72557 1.53416i −0.209488 0.0561320i
\(748\) 0 0
\(749\) −19.1069 34.3973i −0.698152 1.25685i
\(750\) 0 0
\(751\) 21.8309 + 37.8123i 0.796622 + 1.37979i 0.921804 + 0.387656i \(0.126715\pi\)
−0.125182 + 0.992134i \(0.539951\pi\)
\(752\) 0 0
\(753\) −8.46663 31.5979i −0.308541 1.15149i
\(754\) 0 0
\(755\) −0.725941 7.88981i −0.0264197 0.287140i
\(756\) 0 0
\(757\) 7.88896 + 7.88896i 0.286729 + 0.286729i 0.835785 0.549056i \(-0.185013\pi\)
−0.549056 + 0.835785i \(0.685013\pi\)
\(758\) 0 0
\(759\) 18.5337 32.1013i 0.672730 1.16520i
\(760\) 0 0
\(761\) −1.70923 + 0.986825i −0.0619596 + 0.0357724i −0.530660 0.847585i \(-0.678056\pi\)
0.468700 + 0.883357i \(0.344722\pi\)
\(762\) 0 0
\(763\) 33.9593 8.49921i 1.22941 0.307692i
\(764\) 0 0
\(765\) 4.88911 + 0.839490i 0.176766 + 0.0303518i
\(766\) 0 0
\(767\) −0.239397 + 0.0641463i −0.00864413 + 0.00231619i
\(768\) 0 0
\(769\) 17.4914 0.630756 0.315378 0.948966i \(-0.397869\pi\)
0.315378 + 0.948966i \(0.397869\pi\)
\(770\) 0 0
\(771\) 11.7763 0.424112
\(772\) 0 0
\(773\) 43.1933 11.5736i 1.55355 0.416274i 0.622939 0.782271i \(-0.285939\pi\)
0.930616 + 0.365997i \(0.119272\pi\)
\(774\) 0 0
\(775\) −27.7968 + 23.7524i −0.998491 + 0.853212i
\(776\) 0 0
\(777\) 17.2044 + 17.7839i 0.617205 + 0.637994i
\(778\) 0 0
\(779\) −13.9004 + 8.02542i −0.498035 + 0.287540i
\(780\) 0 0
\(781\) 14.3871 24.9193i 0.514813 0.891682i
\(782\) 0 0
\(783\) −19.5716 19.5716i −0.699433 0.699433i
\(784\) 0 0
\(785\) 10.5268 + 8.75286i 0.375717 + 0.312403i
\(786\) 0 0
\(787\) −6.71595 25.0643i −0.239398 0.893445i −0.976117 0.217246i \(-0.930293\pi\)
0.736719 0.676199i \(-0.236374\pi\)
\(788\) 0 0
\(789\) 1.75605 + 3.04156i 0.0625170 + 0.108283i
\(790\) 0 0
\(791\) 0.604323 36.4887i 0.0214873 1.29739i
\(792\) 0 0
\(793\) 1.93688 + 0.518984i 0.0687805 + 0.018